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In the group testing problem we aim to identify a small number of infected individuals within a large population. We avail ourselves to a procedure that can test a group of multiple individuals, with the test result coming out positive iff at least one individual in the group is infected. With all tests conducted in parallel, what is the least number of tests required to identify the status of all individuals? In a recent test design [Aldridge et al. 2016] the individuals are assigned to test groups randomly, with every individual joining an equal number of groups. We pinpoint the sharp threshold for the number of tests required in this randomised design so that it is information-theoretically possible to infer the infection status of every individual. Moreover, we analyse two efficient inference algorithms. These results settle conjectures from [Aldridge et al. 2014, Johnson et al. 2019].
Let $X_i, i in V$ form a Markov random field (MRF) represented by an undirected graph $G = (V,E)$, and $V$ be a subset of $V$. We determine the smallest graph that can always represent the subfield $X_i, i in V$ as an MRF. Based on this result, we
Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information holds the key
In the group testing problem the aim is to identify a small set of $ksim n^theta$ infected individuals out of a population size $n$, $0<theta<1$. We avail ourselves of a test procedure capable of testing groups of individuals, with the test returning
Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations encode exactl
The main contribution of this paper is to design an Information Retrieval (IR) technique based on Algorithmic Information Theory (using the Normalized Compression Distance- NCD), statistical techniques (outliers), and novel organization of data base